To calculate the wavelength of an Antenna the formula for Wavelength is the Speed of Light ~299,792,458 metres per second divided by the frequency in Hertz. However, because electricity travels slower through some materials than others, there is a need to reduce the speed of light by the Velocity of Propagation also commonly known as the Velocity Factor for example a piece of copper wire has a Velocity Factor of 0.951.
Consequently the formula of a full wave antenna at 2.447Ghz (Channel 8) using copper wire is:
(299,792,458 x 0.951) / 2,4470,000,000 = 112mm
A Half Wave antenna would then be 56mm and a Quarter Wave antenna would be 28mm
Please note: This is only a guide to home made antenna building, when looking around the Internet you'll find many variations to this calculation due of a number of reasons ranging from rounding down/up or ways to match the impedance of the antenna with the feed line.
For example feed lines for Transmitters and Transceivers are 50 Ohms so too Wireless LAN equipment. However a half wave dipole is 72 Ohms and a quarter mono pole is 30 Ohms but for maximum efficiency both feed line and antenna must be the same impedance. Consequently there are many tricks employed to achieve a match and no doubt antenna design is a very complex area, but you'll be surprised of what can be done with a little experimentation, specially as the equipment used in Wireless LAN is very low-powered and therefor the risks of equipment damage and interference is minimal and so well worth having a go.